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A129362 a(n) = sum{k=floor((n+1)/2)..n, J(k+1)}, J(n) = A001045(n). 3
1, 1, 4, 8, 19, 37, 80, 160, 331, 661, 1344, 2688, 5419, 10837, 21760, 43520, 87211, 174421, 349184, 698368, 1397419, 2794837, 5591040, 11182080, 22366891, 44733781, 89473024, 178946048, 357903019, 715806037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,0,-2,-4)

FORMULA

G.f.: (1+2x^3)/((1-x-2x^2)(1-x^2-2x^4)).

a(n) = a(n-1) + 3a(n-2) - a(n-3) - 2a(n-5) - 4a(n-6).

a(n) = sum{k=0..floor(n/2), J(n-k+1)}.

a(n) = sum{k=0..n, J(k+1)-J((k+1)/2)(1-(-1)^k)/2}.

a(n) = sum{k=0..n, J(k+1)}-sum{k=0..floor((n-1)/2), J(k+1)}.

MATHEMATICA

LinearRecurrence[{1, 3, -1, 0, -2, -4}, {1, 1, 4, 8, 19, 37}, 30] (* Harvey P. Dale, Oct 22 2011 *)

CROSSREFS

Cf. A129361.

Sequence in context: A130887 A049933 A163318 * A083579 A215112 A265108

Adjacent sequences:  A129359 A129360 A129361 * A129363 A129364 A129365

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 11 2007

STATUS

approved

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Last modified November 21 16:08 EST 2017. Contains 295003 sequences.