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

Author

Colin Barker, Jan 27 2015

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A000566, A001844, A254229, A254230.

Programs

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))

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)).