A253621 -id:A253621 - cp's OEIS frontend

A133272 Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).

1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543

Offset: 1

Richard Choulet, Oct 16 2007

Numbers X such that 140*X^2-140*X+49 is a square.
Also positive integers x in the solutions to 5*x^2 - 7*y^2 - 5*x + 7*y = 0, the corresponding values of y being A253621. - Colin Barker, Jan 06 2015
Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - Colin Barker, Jan 06 2015

Colin Barker, Table of n, a(n) for n = 1..930
Index entries for linear recurrences with constant coefficients, signature (13,-13,1).

Cf. A000566, A069099, A128919, A253621, A253622.

LinearRecurrence[{13,-13,1},{1,7,78},25] (* Paolo Xausa, Jan 07 2024 *)

Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ Colin Barker, Jan 06 2015

a(n+2) = 12*a(n+1) - a(n) - 5.
a(n+1) = 6*a(n) - 5/2 + (1/2)*sqrt(140*a(n)^2 - 140*a(n) + 49).
G.f.: x*(-1+6*x)/((-1+x)*(1-12*x+x^2)). - R. J. Mathar, Nov 14 2007
a(n) = 13*a(n-1) - 13*a(n-2) + a(n-3). - Colin Barker, Jan 06 2015

More terms from Paolo P. Lava, Jul 14 2008

A253622 Centered heptagonal numbers (A069099) which are also centered pentagonal numbers (A005891).

Original entry on oeis.org

1, 106, 15016, 2132131, 302747551, 42988020076, 6103996103206, 866724458635141, 123068769130086781, 17474898492013687726, 2481312517096813570276, 352328902529255513291431, 50028222846637186073812891, 7103655315319951166968139056

Offset: 1

Colin Barker, Jan 06 2015

			106 is in the sequence because it is the 6th centered heptagonal number and the 7th centered pentagonal number.

Colin Barker, Table of n, a(n) for n = 1..465
Index entries for linear recurrences with constant coefficients, signature (143,-143,1).

Cf. A005891, A069099, A133272, A253621.

LinearRecurrence[{143,-143,1},{1,106,15016},20] (* Harvey P. Dale, Feb 25 2016 *)

Vec(-x*(x^2-37*x+1)/((x-1)*(x^2-142*x+1)) + O(x^100))

a(n) = 143*a(n-1)-143*a(n-2)+a(n-3).
G.f.: -x*(x^2-37*x+1) / ((x-1)*(x^2-142*x+1)).
a(n) = (4+(6+sqrt(35))*(71+12*sqrt(35))^(-n)-(-6+sqrt(35))*(71+12*sqrt(35))^n)/16. - Colin Barker, Mar 07 2016

cp's OEIS Frontend

A133272 Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).

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