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A292443 a(n) = (5/32)*A000045(6*n)^2. 0
0, 10, 3240, 1043290, 335936160, 108170400250, 34830532944360, 11215323437683690, 3611299316401203840, 1162827164557749952810, 374426735688279083601000, 120564246064461307169569210, 38821312806020852629517684640, 12500342159292650085397524884890 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Every term is a triangular number. [Problem B-967 in Euler and Sadek, 2003; solution in Euler and Sadek, 2004]

LINKS

Table of n, a(n) for n=0..13.

Russ Euler and Jawad Sadek, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 41, No. 5 (2003), 466-471.

Russ Euler and Jawad Sadek, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 42, No. 3 (2004), 277-282.

FORMULA

Conjectures from Colin Barker, Sep 16 2017: (Start)

G.f.: 10*x*(1 + x) / ((1 - x)*(1 - 322*x + x^2)).

a(n) = ((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)^2) / 32.

a(n) = 323*a(n-1) - 323*a(n-2) + a(n-3) for n > 2.

(End)

MATHEMATICA

Table[(5/32) Fibonacci[6 n]^2, {n, 0, 13}] (* Michael De Vlieger, Sep 16 2017 *)

PROG

(PARI) a(n) = (5/32)*fibonacci(6*n)^2

CROSSREFS

Cf. A000045.

Subsequence of A000217.

Sequence in context: A225764 A243008 A133198 * A001329 A007101 A007103

Adjacent sequences:  A292440 A292441 A292442 * A292444 A292445 A292446

KEYWORD

nonn,easy

AUTHOR

Felix Fröhlich, Sep 16 2017

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)