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A259163 Positive heptagonal numbers (A000566) that are triangular numbers (A000217) divided by 2. 3
18, 189, 37727235, 393298308, 78448579122960, 817809556618215, 163122994382238923193, 1700522115268371779430, 339191755844562643229618814, 3536001066647854270462804353, 705302447816298343956844397692383, 7352626249945315029422809413582264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A000566 and A074378 (even triangular numbers divided by 2). - Michel Marcus, Jun 20 2015

LINKS

Colin Barker, Table of n, a(n) for n = 1..317

Index entries for linear recurrences with constant coefficients, signature (1,2079362,-2079362,-1,1).

FORMULA

G.f.: -9*x*(2*x^4+19*x^3+33170*x^2+19*x+2) / ((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)).

EXAMPLE

18 is in the sequence because 18 is the 3rd heptagonal number, and 2*18 is the 8th triangular number.

MATHEMATICA

LinearRecurrence[{1, 2079362, -2079362, -1, 1}, {18, 189, 37727235, 393298308, 78448579122960}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

PROG

(PARI) Vec(-9*x*(2*x^4+19*x^3+33170*x^2+19*x+2)/((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)) + O(x^20))

CROSSREFS

Cf. A000217, A000566, A074378, A259156-A259162, A259164-A259167.

Sequence in context: A036219 A022646 A268447 * A004314 A125406 A318161

Adjacent sequences:  A259160 A259161 A259162 * A259164 A259165 A259166

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jun 19 2015

STATUS

approved

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Last modified November 20 23:06 EST 2019. Contains 329348 sequences. (Running on oeis4.)