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A227978
a(0)=1, a(1)=2; for n>1, a(n) = n*(2^n+4)/4.
1
1, 2, 4, 9, 20, 45, 102, 231, 520, 1161, 2570, 5643, 12300, 26637, 57358, 122895, 262160, 557073, 1179666, 2490387, 5242900, 11010069, 23068694, 48234519, 100663320, 209715225, 436207642, 905969691, 1879048220, 3892314141, 8053063710, 16642998303
OFFSET
0,2
COMMENTS
The inverse binomial transform of A176328/A176591 (see Comments field in A228827) begins: 1, -2, 25/6, -9, 599/30, -45, 4285/42, -231, 15599/30, -1161, 169625/66, ... Consider these values without sign and the fractions rounded to the nearest integer, the sequence lists the resulting numbers.
Differences table of a(n):
1, 2, 4, 9, 20, 45, 102, 231, 520, 1161, ...
1, 2, 5, 11, 25, 57, 129, 289, 641, 1409, ... After 2: 2^m*(m+4)+1.
1, 3, 6, 14, 32, 72, 160, 352, 768, 1664, ... A078836 (after 3).
2, 3, 8, 18, 40, 88, 192, 416, 896, 1920, ... A129955.
1, 5, 10, 22, 48, 104, 224, 480, 1024, 2176, ... A079861 (after 5).
4, 5, 12, 26, 56, 120, 256, 544, 1152, 2432, ... After 5: 2^m*(m+12).
1, 7, 14, 30, 64, 136, 288, 608, 1280, 2688, ... After 7: 2^m*(m+14).
6, 7, 16, 34, 72, 152, 320, 672, 1408, 2944, ..., etc.
(n-1)*a(n)-n*a(n-1) = A001788(n-1) for n>1. [Bruno Berselli, Oct 11 2013]
FORMULA
a(2n+2) = A229135(n+1); a(2n-1) = -A228767(n) for n>0.
a(n) = 6*a(n-1) -13*a(n-2) +12*a(n-3) -4*a(n-4) for n>5.
G.f.: (1-4*x+5*x^2-x^3-2*x^4+2*x^5)/((1-x)^2*(1-2*x)^2). - Colin Barker, Oct 09 2013
MATHEMATICA
Join[{1, 2}, Table[n (2^n + 4)/4, {n, 2, 40}]] (* Bruno Berselli, Oct 11 2013 *)
PROG
(Magma) [1, 2] cat [n*(2^n+4)/4: n in [2..40]]; // Bruno Berselli, Oct 11 2013
(PARI) a(n) = if (n == 0, 1, if (n == 1, 2, n*(2^n+4)/4)); \\ Michel Marcus, Oct 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 07 2013
EXTENSIONS
More terms from Colin Barker, Oct 09 2013
STATUS
approved