A253920 Indices of centered octagonal numbers (A016754) which are also heptagonal numbers (A000566).

1, 5, 39, 760, 6494, 55518, 1095199, 9363623, 80056197, 1579275478, 13502337152, 115440979836, 2277314143357, 19470360808841, 166465812866595, 3283885415444596, 28076246784010850, 240043586712649434, 4735360491756963355, 40485928392182836139

Offset: 1

Author

Colin Barker, Jan 19 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 3*x + 8*y - 2 = 0, the corresponding values of x being A046195.

Examples

			5 is in the sequence because the 5th centered octagonal number is 81, which is also the 6th heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..950
• Index entries for linear recurrences with constant coefficients, signature (1,0,1442,-1442,0,-1,1).

Crossrefs

Cf. A000566, A016754, A046195, A036354.

Programs

Magma

I:=[1,5,39,760,6494,55518,1095199]; [n le 7 select I[n] else Self(n-1)+1442*Self(n-3)-1442*Self(n-4)-Self(n-6)+Self(n-7): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015

Mathematica

CoefficientList[Series[(4 x^5 + 34 x^4 + 721 x^3 - 34 x^2 -4 x - 1)/((x-1) (x^6 - 1442 x^3 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)
LinearRecurrence[{1,0,1442,-1442,0,-1,1},{1,5,39,760,6494,55518,1095199},20] (* Harvey P. Dale, Jul 04 2017 *)

PARI

Vec(x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1)/((x-1)*(x^6-1442*x^3+1)) + O(x^100))

Formula

a(n) = a(n-1)+1442*a(n-3)-1442*a(n-4)-a(n-6)+a(n-7).

G.f.: x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1) / ((x-1)*(x^6-1442*x^3+1)).

Extensions

Corrected by Vincenzo Librandi, Jan 20 2015