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A178073 Partial sums of sequence A177342. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 14:50 EDT 2019. Contains 328223 sequences. (Running on oeis4.)