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A179903 (1, 3, 5, 7, 9...) convolved with (1, 0, 3, 5, 7, 9,...) 1
1, 3, 8, 21, 46, 87, 148, 233, 346, 491, 672, 893, 1158, 1471, 1836, 2257, 2738, 3283, 3896, 4581, 5342, 6183, 7108, 8121, 9226, 10427, 11728, 13133, 14646, 16271, 18012, 19873, 21858, 23971, 26216, 28597, 31118, 33783, 36596, 39561, 42682, 45963 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Guo-Niu Han, Enumeration of Standard Puzzles

Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]

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

FORMULA

(1 + 3x + 8x^2 + 21x^3 + ...) = (1 + 3x + 5x^2 + 7x^3 + 9x^4 + ...) * (1 + 3x^2 + 5x^3 + 7x^4 + 9x^5 + ...).

a(n) = 2+A005900(n), n>0. G.f.: -(1+x)*(x^3-4*x^2+2*x-1)/(x-1)^4. [From R. J. Mathar, Aug 13 2010]

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jul 04 2012

EXAMPLE

a(5) = 46 = (9, 7, 5, 3, 1) dot (1, 0, 3, 5, 7) = (9 + 0 + 15 + 15 + 7).

MATHEMATICA

CoefficientList[Series[-(1+x)*(x^3-4*x^2+2*x-1)/(x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)

PROG

(MAGMA) I:=[1, 3, 8, 21, 46]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jul 04 2012

CROSSREFS

Sequence in context: A101332 A007773 A071078 * A193045 A238831 A322059

Adjacent sequences:  A179900 A179901 A179902 * A179904 A179905 A179906

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jul 31 2010

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)