A133327 Indices of the 7-gonal numbers that are the sum of 2 consecutive 7-gonal numbers.

1, 241, 19265, 9435905, 755214769, 369906335809, 29605929343313, 14501068166936753, 1160611641361329697, 568470873910348243537, 45498297535040917426721, 22285195184532403676188961, 1783624258808062403600975185, 873624221055568415003611393825

Offset

1,2

Comments

Also nonnegative integers y in the solution to 10*x^2 - 5*y^2 + 4*x + 3*y + 2 = 0, the corresponding values of x being A133328.

Links

Colin Barker, Table of n, a(n) for n = 1..436

Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Polygonal Balancing Numbers I, Integers 22 (2022), A54. See p. 8.

Index entries for linear recurrences with constant coefficients, signature (1,39202,-39202,-1,1).

Formula

The bisections modulo 2 satisfy the same recurrence relation: a(n+2) = 39202*a(n+1) - a(n) - 11760.

G.f.: -x*(17*x^4+8160*x^3-20178*x^2+240*x+1) / ((x-1)*(x^2-198*x+1)*(x^2+198*x+1)). - Colin Barker, Dec 05 2014

Mathematica

LinearRecurrence[{1, 39202, -39202, -1, 1}, {1, 241, 19265, 9435905, 755214769}, 14] (* Michael De Vlieger, Jan 19 2026 *)

Prog

(PARI) Vec(-x*(17*x^4+8160*x^3-20178*x^2+240*x+1)/((x-1)*(x^2-198*x+1)*(x^2+198*x+1)) + O(x^100)) \\ Colin Barker, Dec 05 2014

Crossrefs

Cf. A133324, A133328.

Sequence in context: A008349 A094732 A119728 * A001361 A206842 A206834

Adjacent sequences: A133324 A133325 A133326 * A133328 A133329 A133330

Keyword

nonn,easy

Author

Richard Choulet, Oct 18 2007

Extensions

More terms from Colin Barker, Dec 05 2014

Status

approved