A187673 Partial sums of the tricapped prism numbers A005920.

1, 10, 43, 125, 290, 581, 1050, 1758, 2775, 4180, 6061, 8515, 11648, 15575, 20420, 26316, 33405, 41838, 51775, 63385, 76846, 92345, 110078, 130250, 153075, 178776, 207585, 239743, 275500, 315115, 358856

Offset: 0

Author

Jonathan Vos Post, Mar 12 2011

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A005920.

Programs

Mathematica

Accumulate[LinearRecurrence[{4,-6,4,-1},{1,9,33,82},40]] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,10,43,125,290},40] (* Harvey P. Dale, Feb 15 2015 *)

Formula

a(n) = Sum_{i=0..n} A005920(i).

a(n) = (n+2)*(n+1)*(9*n^2 + 19*n + 12)/24.

a(n) = A002419(n+1) + A050534(n+1).

G.f.: ( -1-5*x-3*x^2 ) / (x-1)^5. - R. J. Mathar, Mar 29 2011

Extensions

Typo in formula fixed by Colin Barker, Apr 19 2013