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A085786 a(n) = A000217(n) + n^3. 4
2, 11, 33, 74, 140, 237, 371, 548, 774, 1055, 1397, 1806, 2288, 2849, 3495, 4232, 5066, 6003, 7049, 8210, 9492, 10901, 12443, 14124, 15950, 17927, 20061, 22358, 24824, 27465, 30287, 33296, 36498, 39899, 43505, 47322, 51356, 55613, 60099, 64820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = n*(2*n^2 + n + 1)/2.

From Colin Barker, Jan 20 2014: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: x*(x+1)*(x+2) / (x-1)^4. (End)

E.g.f.: (x/2)*(4 + 7*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 24 2017

MATHEMATICA

CoefficientList[Series[(x + 1) (x + 2) / (x - 1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 11, 33, 74}, 40] (* Vincenzo Librandi, Aug 14 2017 *)

PROG

(PARI) t(n)=n*(n+1)/2 for(i=1, 40, print1(", "t(i)+i^3))

(MAGMA) [n*(2*n^2 + n + 1)/2: n in [1..40]]; // Vincenzo Librandi, Aug 14 2017

CROSSREFS

Cf. A000217 [t(n)], A000096 [t(n)+n], A005449 [t(n)+n^2].

a(n) = A110449(n, n).

Sequence in context: A173707 A192347 A031400 * A034128 A034427 A056368

Adjacent sequences:  A085783 A085784 A085785 * A085787 A085788 A085789

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jul 23 2003

STATUS

approved

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Last modified October 22 05:06 EDT 2018. Contains 316432 sequences. (Running on oeis4.)