A130566 Pyramidal 47-gonal numbers.

1, 48, 186, 460, 915, 1596, 2548, 3816, 5445, 7480, 9966, 12948, 16471, 20580, 25320, 30736, 36873, 43776, 51490, 60060, 69531, 79948, 91356, 103800, 117325, 131976, 147798, 164836, 183135, 202740, 223696, 246048, 269841, 295120, 321930, 350316, 380323, 411996

Offset: 0

Author

N. J. A. Sloane, Oct 06 2007, based on a suggestion from an unknown correspondent in 2004

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000217.

Programs

Magma

I:=[1, 48, 186, 460]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 29 2012

Mathematica

CoefficientList[Series[(1+44*x)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jun 29 2012 *)
LinearRecurrence[{4,-6,4,-1},{1,48,186,460},40] (* Harvey P. Dale, Jul 07 2025 *)

Formula

a(n) = (15*n + 1)*(n + 2)*(n + 1)/2.

G.f.: (1+44*x)/(1-x)^4. - Colin Barker, Apr 30 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012

From Elmo R. Oliveira, Aug 04 2025: (Start)

E.g.f.: exp(x)*(15*x^3 + 91*x^2 + 94*x + 2)/2.

a(n) = (15*n+1)*A000217(n+1). (End)