A257052 a(n) = cpg(3, n) + cpg(4, n) + ... + cpg(n, n) where cpg(m, n) is the n-th m-th-order centered polygonal number.

0, 0, 0, 10, 44, 123, 274, 530, 930, 1519, 2348, 3474, 4960, 6875, 9294, 12298, 15974, 20415, 25720, 31994, 39348, 47899, 57770, 69090, 81994, 96623, 113124, 131650, 152360, 175419, 200998, 229274, 260430, 294655, 332144, 373098, 417724, 466235, 518850

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^4-7*n^2+10*n-8)/4 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.: x^3*(x^3-3*x^2+6*x-10) / (x-1)^5.

Example

a(4) = cpg(3, 4) + cpg(4, 4) = 19 + 25 = 44.

Mathematica

CoefficientList[Series[x^3 (x^3 - 3 x^2 + 6 x - 10) / (x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 15 2015 *)

Prog

(PARI) cpg(m, n) = m*n*(n-1)/2+1
vector(50, n, n--; sum(m=3, n, cpg(m, n)))
(Magma) [0, 0] cat [(n^4-7*n^2+10*n-8)/4 : n in [2..40]]; // Vincenzo Librandi, Apr 15 2015

Crossrefs

Cf. A241452, A245679, A257051.

Sequence in context: A057517 A126964 A256050 * A008532 A085582 A058310

Adjacent sequences: A257049 A257050 A257051 * A257053 A257054 A257055

Keyword

nonn,easy

Author

Colin Barker, Apr 15 2015

Status

approved