A254652 Indices of pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).

1, 4, 88, 421, 9661, 46288, 1062604, 5091241, 116876761, 559990204, 12855381088, 61593831181, 1413975042901, 6774761439688, 155524399338004, 745162164534481, 17106269952137521, 81961063337353204, 1881534170335789288, 9014971804944317941

Offset

1,2

Comments

Also positive integers x in the solutions to 3*x^2 - 7*y^2 - x + 7*y - 2 = 0, the corresponding values of y being A254653.

Links

Colin Barker, Table of n, a(n) for n = 1..980

Index entries for linear recurrences with constant coefficients, signature (1,110,-110,-1,1).

Formula

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^2-4*x+1)*(x^2+7*x+1) / ((x-1)*(x^4-110*x^2+1)).

Example

4 is in the sequence because the 4th pentagonal number is 22, which is also the 3rd centered heptagonal number.

Mathematica

LinearRecurrence[{1, 110, -110, -1, 1}, {1, 4, 88, 421, 9661}, 30] (* Harvey P. Dale, Dec 09 2018 *)

Prog

(PARI) Vec(-x*(x^2-4*x+1)*(x^2+7*x+1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

Crossrefs

Cf. A000326, A069099, A254653, A254654.

Sequence in context: A122209 A059577 A239007 * A028554 A303153 A154137

Adjacent sequences: A254649 A254650 A254651 * A254653 A254654 A254655

Keyword

nonn,easy

Author

Colin Barker, Feb 04 2015

Status

approved