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

Author

Bruno Berselli, May 31 2010

Keywords

• nonn
• easy

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).

Programs

Magma

A177342:=func; [&+[A177342(i): i in [1..n]]: n in [1..35]]; // Bruno Berselli, Jun 21 2012

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{1,10,41,116,265},40] (* Harvey P. Dale, Feb 02 2025 *)

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]

Extensions

Edited by Bruno Berselli, Dec 29 2010