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

0,2

Links

Table of n, a(n) for n=0..30.

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

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

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 *)

Crossrefs

Cf. A005920.

Sequence in context: A336288 A211070 A251936 * A297655 A198695 A227728

Adjacent sequences: A187670 A187671 A187672 * A187674 A187675 A187676

Keyword

nonn,easy

Author

Jonathan Vos Post, Mar 12 2011

Extensions

Typo in formula fixed by Colin Barker, Apr 19 2013

Status

approved