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A254962 Indices of hexagonal numbers (A000384) that are also centered pentagonal numbers (A005891). 3
1, 2, 12, 31, 211, 552, 3782, 9901, 67861, 177662, 1217712, 3188011, 21850951, 57206532, 392099402, 1026529561, 7035938281, 18420325562, 126254789652, 330539330551, 2265550275451, 5931287624352, 40653650168462, 106432637907781, 729500152756861 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 4*x^2 - 5*y^2 - 2*x + 5*y - 2 = 0, the corresponding values of y being A254627.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,18,-18,-1,1).

FORMULA

a(n) = a(n-1)+18*a(n-2)-18*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+x^3-8*x^2+x+1) / ((x-1)*(x^2-4*x-1)*(x^2+4*x-1)).

a(n) = (2 + (2-r)^n - (-2-r)^n*(-2+r) + 2*(-2+r)^n + r*(-2+r)^n + (2+r)^n)/8 where r = sqrt(5). - Colin Barker, Nov 25 2016

a(n+2) - a(n) = A000032(3*n + 2) if n is odd, A000032(3*n + 1) if n is even. - Diego Rattaggi, May 11 2020

EXAMPLE

12 is in the sequence because the 12th hexagonal number is 276, which is also the 11th centered pentagonal number.

PROG

(PARI) Vec(-x*(x^4+x^3-8*x^2+x+1)/((x-1)*(x^2-4*x-1)*(x^2+4*x-1)) + O(x^100))

CROSSREFS

Cf. A000032 (Lucas numbers), A000384, A005891, A254627, A254628.

Sequence in context: A101177 A117625 A297763 * A139323 A225525 A240395

Adjacent sequences:  A254959 A254960 A254961 * A254963 A254964 A254965

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Feb 11 2015

STATUS

approved

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Last modified August 16 11:28 EDT 2022. Contains 356168 sequences. (Running on oeis4.)