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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 (list; graph; refs; listen; history; text; internal format)
 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 A329276 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

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Last modified December 7 18:12 EST 2019. Contains 329847 sequences. (Running on oeis4.)