A015221 Odd square pyramidal numbers.

1, 5, 55, 91, 285, 385, 819, 1015, 1785, 2109, 3311, 3795, 5525, 6201, 8555, 9455, 12529, 13685, 17575, 19019, 23821, 25585, 31395, 33511, 40425, 42925, 51039, 53955, 63365, 66729, 77531, 81375, 93665, 98021, 111895, 116795, 132349, 137825, 155155, 161239, 180441

Offset

0,2

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

Odd numbers in A000330.

From Ant King, Oct 17 2012: (Start)

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + 128.

a(n) = (1 + 4*n + (-1)^n)*(2 + 4*n + (-1)^n)*(3 + 4*n + (-1)^n)/24.

G.f.: (1+4*x+47*x^2+24*x^3+47*x^4+4*x^5+x^6)/((1-x)^4*(1+x)^3). (End)

From Amiram Eldar, Mar 07 2022: (Start)

Sum_{n>=0} 1/a(n) = 6*sqrt(2)*log(sqrt(2)+1) - 9*log(2).

Sum_{n>=0} (-1)^n/a(n) = 3*Pi*(1-2*tan(Pi/8))/2. (End)

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 5, 55, 91, 285, 385, 819}, 38] (* Ant King Oct 17 2012 *)

Crossrefs

Cf. A000330, A015222.

Sequence in context: A244439 A216446 A307991 * A035305 A292455 A292735

Adjacent sequences: A015218 A015219 A015220 * A015222 A015223 A015224

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman

Status

approved