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A193828 Even generalized pentagonal numbers. 3
0, 2, 12, 22, 26, 40, 70, 92, 100, 126, 176, 210, 222, 260, 330, 376, 392, 442, 532, 590, 610, 672, 782, 852, 876, 950, 1080, 1162, 1190, 1276, 1426, 1520, 1552, 1650, 1820, 1926, 1962, 2072, 2262, 2380, 2420, 2542, 2752, 2882, 2926, 3060, 3290, 3432, 3480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Even numbers in A001318.

REFERENCES

M. Merca, The bisectional pentagonal number theorem, Journal of Number Theory, Volume 157, December 2015, Pages 223-232

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1).

FORMULA

a(n) = A000217(A108752(n+1))/3 = 2*A154293(n+1).

G.f.: -2*x*(x^2-x+1)*(x^2+4*x+1)/((x-1)^3*(x^2+1)^2). - Colin Barker, Sep 12 2012

MATHEMATICA

CoefficientList[Series[-2*x*(x^2 - x + 1)*(x^2 + 4*x + 1)/((x - 1)^3*(x^2 + 1)^2), {x, 0, 50}], x] (* G. C. Greubel, Jun 06 2017 *)

LinearRecurrence[{3, -5, 7, -7, 5, -3, 1}, {0, 2, 12, 22, 26, 40, 70}, 50] (* Harvey P. Dale, Apr 09 2019 *)

PROG

(PARI) x='x+O('x^50); concat([0], Vec(-2*x*(x^2-x+1)*(x^2+4*x+1)/((x-1)^3*(x^2+1)^2))) \\ G. C. Greubel, Jun 06 2017

CROSSREFS

Cf. A001318, A067589.

Sequence in context: A077410 A211029 A225188 * A191226 A063599 A163479

Adjacent sequences:  A193825 A193826 A193827 * A193829 A193830 A193831

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Aug 19 2011

STATUS

approved

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Last modified September 17 08:54 EDT 2019. Contains 327127 sequences. (Running on oeis4.)