A227978 a(0)=1, a(1)=2; for n>1, a(n) = n*(2^n+4)/4.

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]

Links

Bruno Berselli, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

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

Cf. A001788, A079862, A079863.

Sequence in context: A052534 A213411 A080135 * A206741 A167750 A343756

Adjacent sequences: A227975 A227976 A227977 * A227979 A227980 A227981

Keyword

nonn,easy

Author

Paul Curtz, Oct 07 2013

Extensions

More terms from Colin Barker, Oct 09 2013

Status

approved