A178073 Partial sums of sequence A177342.

1, 10, 41, 116, 265, 526, 945, 1576, 2481, 3730, 5401, 7580, 10361, 13846, 18145, 23376, 29665, 37146, 45961, 56260, 68201, 81950, 97681, 115576, 135825, 158626, 184185, 212716, 244441, 279590, 318401, 361120, 408001, 459306, 515305

Offset

1,2

Comments

a(n)==1 (mod n+1). E.g., a(4)=116 and 116==1 (mod 5), a(11)=5401 and 5401==1 (mod 12).

Inverse binomial transform of this sequence: 1, 9, 22, 22, 8, 0, 0 (0 continued).

Links

B. Berselli, Table of n, a(n) for n = 1..10000.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n*(n^3+n^2+2*n-1)/3.

G.f.: x*(1+5*x+x^2+x^3)/(1-x)^5.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) with n>5.

a(n)+a(-n) = A035598(n). [Bruno Berselli, Jun 21 2012]

Prog

(Magma) A177342:=func<n | (4*n^3-3*n^2+5*n-3)/3>; [&+[A177342(i): i in [1..n]]: n in [1..35]]; // Bruno Berselli, Jun 21 2012

Crossrefs

Sequence in context: A246972 A266396 A006323 * A102784 A294604 A061003

Adjacent sequences: A178070 A178071 A178072 * A178074 A178075 A178076

Keyword

nonn,easy

Author

Bruno Berselli, May 31 2010

Extensions

Edited by Bruno Berselli, Dec 29 2010

Status

approved