A061223 a(n) = n^3 + (n + 1)^4 + (n + 2)^5.

33, 260, 1113, 3408, 8465, 18228, 35385, 63488, 107073, 171780, 264473, 393360, 568113, 799988, 1101945, 1488768, 1977185, 2585988, 3336153, 4250960, 5356113, 6679860, 8253113, 10109568, 12285825, 14821508, 17759385, 21145488, 25029233

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

From Bruno Berselli, Aug 05 2011: (Start)

G.f.: (33 + 62*x + 48*x^2 - 30*x^3 + 7*x^4)/(1-x)^6.

a(n) = (n+1)*(n^4 + 10*n^3 + 35*n^2 + 51*n + 33).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). (End)

E.g.f.: (33 + 227*x + 313*x^2 + 136*x^3 + 21*x^4 + x^5)*exp(x). - Stefano Spezia, Nov 02 2018

Example

For n=1, a(1) = 1 + 2^4 + 3^5 = 1 + 16 + 243 = 260.

Maple

seq(k^3+(k+1)^4+(k+2)^5, k=0..30); # Muniru A Asiru, Nov 02 2018

Mathematica

#[[1]]^3+#[[2]]^4+#[[3]]^5&/@Partition[Range[0, 30], 3, 1] (* Harvey P. Dale, Jul 23 2012 *)
Table[(n+1)*(n^4 +10*n^3 +35*n^2 +51*n +33), {n, 0, 30}] (* G. C. Greubel, Nov 02 2018 *)
CoefficientList[Series[E^x (33 + 227 x + 313 x^2 + 136 x^3 + 21 x^4 + x^5), {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 02 2018 *)

Prog

(Magma) [n^3+(n+1)^4+(n+2)^5: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011
(PARI) vector(30, n, n--; (n+1)*(n^4 +10*n^3 +35*n^2 +51*n +33)) \\ G. C. Greubel, Nov 02 2018
(GAP) List([0..30], k->k^3+(k+1)^4+(k+2)^5); # Muniru A Asiru, Nov 02 2018

Crossrefs

Sequence in context: A197347 A344524 A197398 * A119782 A252978 A268264

Adjacent sequences: A061220 A061221 A061222 * A061224 A061225 A061226

Keyword

nonn,easy

Author

Olivier Gérard, May 31 2001

Extensions

Offset changed from 1 to 0 by Vincenzo Librandi, Aug 05 2011

Status

approved