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A254674 Indices of heptagonal numbers (A000566) which are also centered triangular numbers (A005448). 3
1, 10, 34, 601, 2089, 37234, 129466, 2307889, 8024785, 143051866, 497407186, 8866907785, 30831220729, 549605230786, 1911038277994, 34066657400929, 118453542014881, 2111583153626794, 7342208566644610, 130884088867460281, 455098477589950921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 5*x^2 - 3*y^2 - 3*x + 3*y - 2 = 0, the corresponding values of y being A254675.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,62,-62,-1,1).

FORMULA

a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+9*x^3-38*x^2+9*x+1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).

EXAMPLE

10 is in the sequence because the 10th heptagonal number is 235, which is also the 13th centered triangular number.

PROG

(PARI) Vec(-x*(x^4+9*x^3-38*x^2+9*x+1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))

CROSSREFS

Cf. A000566, A005448, A254675, A254676.

Sequence in context: A219591 A272365 A230895 * A260336 A010818 A243939

Adjacent sequences:  A254671 A254672 A254673 * A254675 A254676 A254677

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Feb 05 2015

STATUS

approved

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Last modified April 12 09:39 EDT 2021. Contains 342920 sequences. (Running on oeis4.)