Sequences

392,541 sequences

a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1, with a(0) = 1, a(1) = 2.A001510
a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1, with a(0) = 1, a(1) = 2.
The ruler function: exponent of the highest power of 2 dividing 2n. Equivalently, the 2-adic valuation of 2n.A001511
The ruler function: exponent of the highest power of 2 dividing 2n. Equivalently, the 2-adic valuation of 2n.
a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).A001512
a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).
a(n) = (6*n+1)*(6*n+5).A001513
a(n) = (6*n+1)*(6*n+5).
Bessel polynomial {y_n}'(1).A001514
Bessel polynomial {y_n}'(1).
Bessel polynomial y_n(x) evaluated at x=1.A001515
Bessel polynomial y_n(x) evaluated at x=1.
Bessel polynomial {y_n}''(1).A001516
Bessel polynomial {y_n}''(1).
Bessel polynomials y_n(x) (see A001498) evaluated at 2.A001517
Bessel polynomials y_n(x) (see A001498) evaluated at 2.
Bessel polynomial y_n(3).A001518
Bessel polynomial y_n(3).
a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1.A001519
a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1.
a(n) = (6*n+1)*(6*n+3)*(6*n+5).A001520
a(n) = (6*n+1)*(6*n+3)*(6*n+5).
a(1) = 1; thereafter a(n+1) = floor(sqrt(2*a(n)*(a(n)+1))).A001521
a(1) = 1; thereafter a(n+1) = floor(sqrt(2*a(n)*(a(n)+1))).
Number of n-stacks with strictly receding walls, or the number of Type A partitions of n in the sense of Auluck (1951).A001522
Number of n-stacks with strictly receding walls, or the number of Type A partitions of n in the sense of Auluck (1951).
Number of stacks, or planar partitions of n; also weakly unimodal compositions of n.A001523
Number of stacks, or planar partitions of n; also weakly unimodal compositions of n.
Number of stacks, or arrangements of n pennies in contiguous rows, each touching 2 in row below.A001524
Number of stacks, or arrangements of n pennies in contiguous rows, each touching 2 in row below.
a(n) = (3n)!/(3!n!).A001525
a(n) = (3n)!/(3!n!).
a(n) = (7*n+1)*(7*n+6).A001526
a(n) = (7*n+1)*(7*n+6).
a(n) = 2 * Sum_{i=0..n} C(2^n-1, i).A001527
a(n) = 2 * Sum_{i=0..n} C(2^n-1, i).
NPN-equivalence classes of switching functions of exactly n variables.A001528
NPN-equivalence classes of switching functions of exactly n variables.
NPN-equivalence classes of threshold functions of n or fewer variables.A001529
NPN-equivalence classes of threshold functions of n or fewer variables.
NPN-equivalence classes of threshold functions of exactly n variables.A001530
NPN-equivalence classes of threshold functions of exactly n variables.
Number of self-dual Boolean functions of n variables that are distinct under complementation/permutation.A001531
Number of self-dual Boolean functions of n variables that are distinct under complementation/permutation.
Number of NP-equivalence classes of self-dual threshold functions of n or fewer variables; number of majority (i.e., decisive and weighted) games with n players.A001532
Number of NP-equivalence classes of self-dual threshold functions of n or fewer variables; number of majority (i.e., decisive and weighted) games with n players.
a(n) = (8*n+1)*(8*n+7).A001533
a(n) = (8*n+1)*(8*n+7).
a(n) = (9*n+1)*(9*n+8).A001534
a(n) = (9*n+1)*(9*n+8).
a(n) = (10n+1)*(10n+9).A001535
a(n) = (10n+1)*(10n+9).
a(n) = (11*n+1)*(11*n+10).A001536
a(n) = (11*n+1)*(11*n+10).
Invertible Boolean functions with AG(n,2) acting on the domain and range.A001537
Invertible Boolean functions with AG(n,2) acting on the domain and range.
a(n) = (12*n+1)*(12*n+11).A001538
a(n) = (12*n+1)*(12*n+11).
a(n) = (4*n+1)*(4*n+3).A001539
a(n) = (4*n+1)*(4*n+3).
Number of transpositions needed to generate permutations of length n.A001540
Number of transpositions needed to generate permutations of length n.
a(0) = 1, a(1) = 3; for n > 1, a(n) = 6*a(n-1) - a(n-2).A001541
a(0) = 1, a(1) = 3; for n > 1, a(n) = 6*a(n-1) - a(n-2).
a(n) = 6*a(n-1) - a(n-2) for n > 1, a(0)=0 and a(1)=2.A001542
a(n) = 6*a(n-1) - a(n-2) for n > 1, a(0)=0 and a(1)=2.
a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0.A001543
a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0.
A nonlinear recurrence: a(n) = a(n-1)^2 - 6*a(n-1) + 6, with a(0) = 1, a(1) = 7.A001544
A nonlinear recurrence: a(n) = a(n-1)^2 - 6*a(n-1) + 6, with a(0) = 1, a(1) = 7.
a(n) = (5*n+1)*(5*n+4).A001545
a(n) = (5*n+1)*(5*n+4).
a(n) = (8*n+1)*(8*n+3)*(8*n+5)*(8*n+7).A001546
a(n) = (8*n+1)*(8*n+3)*(8*n+5)*(8*n+7).
a(n) = (7*n+1)*(7*n+2)*(7*n+4).A001547
a(n) = (7*n+1)*(7*n+2)*(7*n+4).
Number of connected linear spaces with n (unlabeled) points.A001548
Number of connected linear spaces with n (unlabeled) points.
Related to Gilbreath conjecture.A001549
Related to Gilbreath conjecture.
a(n) = 1^n + 2^n + 3^n.A001550
a(n) = 1^n + 2^n + 3^n.
a(n) = 1^n + 2^n + 3^n + 4^n.A001551
a(n) = 1^n + 2^n + 3^n + 4^n.
a(n) = 1^n + 2^n + ... + 5^n.A001552
a(n) = 1^n + 2^n + ... + 5^n.
a(n) = 1^n + 2^n + ... + 6^n.A001553
a(n) = 1^n + 2^n + ... + 6^n.
a(n) = 1^n + 2^n + ... + 7^n.A001554
a(n) = 1^n + 2^n + ... + 7^n.
a(n) = 1^n + 2^n + ... + 8^n.A001555
a(n) = 1^n + 2^n + ... + 8^n.
a(n) = 1^n + 2^n + ... + 9^n.A001556
a(n) = 1^n + 2^n + ... + 9^n.
a(n) = 1^n + 2^n + ... + 10^n.A001557
a(n) = 1^n + 2^n + ... + 10^n.
Number of hill-free Dyck paths of semilength n+3 and having length of first descent equal to 1 (a hill in a Dyck path is a peak at level 1).A001558
Number of hill-free Dyck paths of semilength n+3 and having length of first descent equal to 1 (a hill in a Dyck path is a peak at level 1).
a(0) = 1, a(1) = 4; thereafter a(n)*(2n + 10) - a(n-1)*(11n + 35) + a(n-2)*(8n + 2) + a(n-3)*(15n + 7) + a(n-4)*(4n - 2) = 0.A001559
a(0) = 1, a(1) = 4; thereafter a(n)*(2n + 10) - a(n-1)*(11n + 35) + a(n-2)*(8n + 2) + a(n-3)*(15n + 7) + a(n-4)*(4n - 2) = 0.