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A254137 Indices of centered hexagonal numbers (A003215) which are also pentagonal numbers (A000326). 3
1, 52, 629, 59432, 725289, 68583900, 836982301, 79145760592, 965876849489, 91334139138692, 1114621047327429, 105399517420289400, 1286271722739003001, 121630951768874828332, 1484356453419762135149, 140362012941764131605152, 1712946060974682764958369 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers y in the solutions to 3*x^2 - 6*y^2 - x + 6*y - 2 = 0, the corresponding values of x being A254136.

LINKS

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

FORMULA

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(51*x^3+577*x^2-51*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

EXAMPLE

52 is in the sequence because the 52nd centered hexagonal number is 7957, which is also the 73rd pentagonal number.

PROG

(PARI) Vec(x*(51*x^3+577*x^2-51*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

CROSSREFS

Cf. A000326, A003215, A254136, A254138.

Sequence in context: A285753 A100413 A221272 * A249712 A255945 A215365

Adjacent sequences:  A254134 A254135 A254136 * A254138 A254139 A254140

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 26 2015

STATUS

approved

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Last modified July 6 04:31 EDT 2022. Contains 355108 sequences. (Running on oeis4.)