Number of solutions to a+b+c < d+e with each of a,b,c,d,e in {1..n+1}.

Terms

a(0) =1a(1) =21a(2) =121a(3) =432a(4) =1182a(5) =2723a(6) =5558a(7) =10368a(8) =18039a(9) =29689a(10) =46695a(11) =70720a(12) =103740a(13) =148071a(14) =206396a(15) =281792a(16) =377757a(17) =498237a(18) =647653a(19) =830928a(20) =1053514a(21) =1321419a(22) =1641234a(23) =2020160a(24) =2466035a(25) =2987361a(26) =3593331a(27) =4293856a(28) =5099592a(29) =6021967