A257051 a(n) = cpg(n, 3) + cpg(n, 4) + ... + cpg(n, n) where cpg(n, m) is the m-th n-th-order centered polygonal number.

0, 0, 0, 10, 38, 98, 208, 390, 670, 1078, 1648, 2418, 3430, 4730, 6368, 8398, 10878, 13870, 17440, 21658, 26598, 32338, 38960, 46550, 55198, 64998, 76048, 88450, 102310, 117738, 134848, 153758, 174590, 197470, 222528, 249898, 279718, 312130, 347280, 385318

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Wikipedia, Centered polygonal number

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

Formula

a(n) = (n^4-n^2-12)/6 for n>1.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>6.

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

Example

a(4) = cpg(4, 3) + cpg(4, 4) = 13 + 25 = 38.

Mathematica

CoefficientList[Series[2 x^3 (x^3 - 4 x^2 + 6 x - 5) / (x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 15 2015 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 10, 38, 98, 208}, 40] (* Harvey P. Dale, Dec 26 2015 *)

Prog

(PARI) cpg(m, n) = m*n*(n-1)/2+1
vector(50, n, sum(m=3, n-1, cpg(n-1, m)))
(Magma) [0, 0] cat [(n^4-n^2-12)/6: n in [2..40]]; // Vincenzo Librandi, Apr 15 2015

Crossrefs

Cf. A241452, A245679, A257052.

Sequence in context: A154517 A034859 A197060 * A250420 A136840 A027982

Adjacent sequences: A257048 A257049 A257050 * A257052 A257053 A257054

Keyword

nonn,easy

Author

Colin Barker, Apr 15 2015

Status

approved