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A047732 First differences are A005563. 1
1, 4, 12, 27, 51, 86, 134, 197, 277, 376, 496, 639, 807, 1002, 1226, 1481, 1769, 2092, 2452, 2851, 3291, 3774, 4302, 4877, 5501, 6176, 6904, 7687, 8527, 9426, 10386, 11409, 12497, 13652, 14876, 16171, 17539, 18982, 20502, 22101, 23781 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = A051925(n+1)+1. Alex Ratushnyak, Jun 27 2012

G.f.: (1+2*x^2-x^3)/(1-x)^4. - Vincenzo Librandi, Jun 28 2012

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 28 2012

a(n) = (2*n^3+9*n^2+7*n+6)/6. - Vincenzo Librandi, Jun 28 2012

MATHEMATICA

CoefficientList[Series[(1+2*x^2-x^3)/((1-x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 28 2012 *)

LinearRecurrence[{4, -6, 4, -1}, {1, 4, 12, 27}, 50] (* Harvey P. Dale, Aug 22 2015 *)

PROG

(MAGMA) I:=[1, 4, 12, 27]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 28 2012

CROSSREFS

Sequence in context: A266958 A057306 A212973 * A104385 A213760 A062479

Adjacent sequences:  A047729 A047730 A047731 * A047733 A047734 A047735

KEYWORD

nonn,easy

AUTHOR

Patternfinder(AT)webtv.net (Robert Newstedt)

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)