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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 5 00:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)