A015226 Even hexagonal pyramidal numbers.

22, 50, 252, 372, 946, 1222, 2360, 2856, 4750, 5530, 8372, 9500, 13482, 15022, 20336, 22352, 29190, 31746, 40300, 43460, 53922, 57750, 70312, 74872, 89726, 95082, 112420, 118636, 138650, 145790, 168672, 176800, 202742, 211922, 241116

Offset

0,1

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

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

Formula

Even numbers of form n(n+1)(4n-1)/6.

Contribution from Ant King, Oct 25 2012: (Start)

a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).

a(n) = 3*a(n-2) -3*a(n-4) +a(n-6) +256.

a(n) = (4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24.

G. f. 2*x*(11 + 14*x + 68*x^2 + 18*x^3 + 17*x^4) / ((1-x)^4*(1+x)^3).

(End)

E.g.f.: (1/6)*(3*(15 - 30*x + 8*x^2)*exp(-x) + (87 + 348*x + 228*x^2 + 32*x^3 ) *exp(x)). - G. C. Greubel, Jul 30 2016

Mathematica

Select[ Table[ n(n+1)(4n-1)/6, {n, 100} ], EvenQ ]
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {22, 50, 252, 372, 946, 1222, 2360}, 35] (* Ant King, Oct 25 2012 *)

Prog

(PARI) a(n)=(4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24 \\ Charles R Greathouse IV, Jul 30 2016

Crossrefs

Sequence in context: A039345 A043168 A043948 * A092221 A191279 A200880

Adjacent sequences: A015223 A015224 A015225 * A015227 A015228 A015229

Keyword

nonn,easy

Author

Mohammad K. Azarian, Dec 11 1999

Extensions

More terms from Erich Friedman.

Status

approved