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A130218 Partial sums of A100119. Sum of first n of the n-th centered n-gonal numbers. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A108912 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

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Last modified February 16 02:32 EST 2019. Contains 320140 sequences. (Running on oeis4.)