A130218 Partial sums of A100119. Sum of first n of the n-th centered n-gonal numbers.

1, 3, 10, 29, 70, 146, 273, 470, 759, 1165, 1716, 2443, 3380, 4564, 6035, 7836, 10013, 12615, 15694, 19305, 23506, 28358, 33925, 40274, 47475, 55601, 64728, 74935, 86304, 98920, 112871, 128248, 145145, 163659, 183890, 205941, 229918, 255930

Offset

1,2

Comments

This is to n-th centered n-gonal numbers (A100119) as A101357 is to n-th n-gonal numbers (A060354). a(2) = 3 and a(4) = 29 are primes. a(39) = 284089 = 13^2 * 41^2.

Links

Table of n, a(n) for n=1..38.

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

Formula

a(n) = (n*(26-3*n-2*n^2+3*n^3))/24. G.f.: x*(x^3-5*x^2+2*x-1) / (x-1)^5. - Colin Barker, Apr 29 2013

Example

a(41) = 1 + 2 + 7 + 19 + 41 + 76 + 127 + 197 + 289 + 406 + 551 + 727 + 937 + 1184 + 1471 + 1801 + 2177 + 2602 + 3079 + 3611 + 4201 + 4852 + 5567 + 6349 + 7201 + 8126 + 9127 + 10207 + 11369 + 12616 + 13951 + 15377 + 16897 + 18514 + 20231 + 22051 + 23977 + 26012 + 28159 + 30421 + 32801 + 35302 = 382613.

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 10, 29, 70}, 40] (* Harvey P. Dale, Jun 02 2018 *)

Crossrefs

Cf. A060354, A100119, A101357.

Sequence in context: A361741 A055336 A092325 * A114958 A048493 A269144

Adjacent sequences: A130215 A130216 A130217 * A130219 A130220 A130221

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 04 2007

Status

approved