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A131055 1 followed by repeats of 2*k. 4
1, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68, 68, 70, 70, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..72.

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

FORMULA

Inverse binomial transform of A131056: (1, 3, 7, 17, 41, 97, 225, ...).

a(n) = 1 + Sum{i=0..n} (1 - (-1)^i - (i!^2 mod (i+1))*((i+1)!^2 mod (i+2))), with n >= 0. - Paolo P. Lava, Jul 24 2007

From Colin Barker, Oct 28 2012: (Start)

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

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 1.

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

MAPLE

P:=proc(n) local i, j, k; for i from 0 by 1 to n do j:=1+sum('1-(-1)^k-(k!^2 mod (k+1))*((k+1)!^2 mod (k+2))', 'k'=0..i); print(j); od; end: P(100); # Paolo P. Lava, Jul 24 2007

MATHEMATICA

Join[{1}, Table[2*Floor[i/2], {i, 2, 81}]] (* Stefan Steinerberger, Jun 13 2007 *)

With[{c=2*Range[40]}, Join[{1}, Riffle[c, c]]] (* Harvey P. Dale, Jul 25 2019 *)

CROSSREFS

Cf. A131056.

Sequence in context: A319399 A161764 A293706 * A052928 A137501 A308767

Adjacent sequences:  A131052 A131053 A131054 * A131056 A131057 A131058

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jun 12 2007

EXTENSIONS

More terms from Stefan Steinerberger, Jun 13 2007

STATUS

approved

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)