A254228 Indices of heptagonal numbers (A000566) which are also centered square numbers (A001844).

1, 41, 185, 13105, 59473, 4219673, 19150025, 1358721505, 6166248481, 437504104841, 1985512860761, 140874963037201, 639328974916465, 45361300593873785, 205861944410240873, 14606197916264321473, 66286906771122644545, 4703150367736517640425

Offset

1,2

Comments

Also positive integers x in the solutions to 5*x^2 - 4*y^2 - 3*x + 4*y - 2 = 0, the corresponding values of y being A254229.

Links

Colin Barker, Table of n, a(n) for n = 1..797

Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

Formula

a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+40*x^3-178*x^2+40*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).

Example

41 is in the sequence because the 41st heptagonal number is 4141, which is also the 46th centered square number.

Prog

(PARI) Vec(-x*(x^4+40*x^3-178*x^2+40*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))

Crossrefs

Cf. A000566, A001844, A254229, A254230.

Sequence in context: A282941 A141922 A142080 * A141939 A264653 A297227

Adjacent sequences: A254225 A254226 A254227 * A254229 A254230 A254231

Keyword

nonn,easy

Author

Colin Barker, Jan 27 2015

Status

approved