A253622 Centered heptagonal numbers (A069099) which are also centered pentagonal numbers (A005891).

1, 106, 15016, 2132131, 302747551, 42988020076, 6103996103206, 866724458635141, 123068769130086781, 17474898492013687726, 2481312517096813570276, 352328902529255513291431, 50028222846637186073812891, 7103655315319951166968139056

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..465

Index entries for linear recurrences with constant coefficients, signature (143,-143,1).

Formula

a(n) = 143*a(n-1)-143*a(n-2)+a(n-3).

G.f.: -x*(x^2-37*x+1) / ((x-1)*(x^2-142*x+1)).

a(n) = (4+(6+sqrt(35))*(71+12*sqrt(35))^(-n)-(-6+sqrt(35))*(71+12*sqrt(35))^n)/16. - Colin Barker, Mar 07 2016

Example

106 is in the sequence because it is the 6th centered heptagonal number and the 7th centered pentagonal number.

Mathematica

LinearRecurrence[{143, -143, 1}, {1, 106, 15016}, 20] (* Harvey P. Dale, Feb 25 2016 *)

Prog

(PARI) Vec(-x*(x^2-37*x+1)/((x-1)*(x^2-142*x+1)) + O(x^100))

Crossrefs

Cf. A005891, A069099, A133272, A253621.

Sequence in context: A166912 A223497 A078281 * A184208 A082177 A156020

Adjacent sequences: A253619 A253620 A253621 * A253623 A253624 A253625

Keyword

nonn,easy

Author

Colin Barker, Jan 06 2015

Status

approved