A254709 Indices of pentagonal numbers (A000326) which are also centered square numbers (A001844).

1, 2, 10, 25, 137, 346, 1906, 4817, 26545, 67090, 369722, 934441, 5149561, 13015082, 71724130, 181276705, 998988257, 2524858786, 13914111466, 35166746297, 193798572265, 489809589370, 2699265900242, 6822167504881, 37595924031121, 95020535478962

Offset

1,2

Comments

Also positive integers x in the solutions to 3*x^2 - 4*y^2 - x + 4*y - 2 = 0, the corresponding values of y being A254710.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,14,-14,-1,1).

Formula

a(n) = a(n-1)+14*a(n-2)-14*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+x^3-6*x^2+x+1) / ((x-1)*(x^2-4*x+1)*(x^2+4*x+1)).

Example

10 is in the sequence because the 10th pentagonal number is 145, which is also the 9th centered square number.

Mathematica

LinearRecurrence[{1, 14, -14, -1, 1}, {1, 2, 10, 25, 137}, 30] (* Harvey P. Dale, Aug 08 2017 *)

Prog

(PARI) Vec(-x*(x^4+x^3-6*x^2+x+1)/((x-1)*(x^2-4*x+1)*(x^2+4*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A001844, A254710, A254711.

Sequence in context: A058373 A167386 A027719 * A374180 A069894 A045605

Adjacent sequences: A254706 A254707 A254708 * A254710 A254711 A254712

Keyword

nonn,easy

Author

Colin Barker, Feb 06 2015

Status

approved