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 A116413 Expansion of (1+x)/(1-2x-x^2-x^3). 3
 1, 3, 7, 18, 46, 117, 298, 759, 1933, 4923, 12538, 31932, 81325, 207120, 527497, 1343439, 3421495, 8713926, 22192786, 56520993, 143948698, 366611175, 933692041, 2377943955, 6056191126, 15424018248, 39282171577, 100044552528, 254795294881, 648917313867 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Diagonal sums of number triangle A116412. A078058 is an alternating sign version. LINKS Table of n, a(n) for n=0..29. Index entries for linear recurrences with constant coefficients, signature (2,1,1). FORMULA a(n)=2a(n-1)+a(n-2)+a(n-3); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(k+1,j)C(n-k-j,k)2^(n-2k-j)}}. MATHEMATICA CoefficientList[Series[(1+x)/(1-2x-x^2-x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, 1}, {1, 3, 7}, 50] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *) CROSSREFS Sequence in context: A318899 A114713 A078058 * A052960 A059512 A094297 Adjacent sequences: A116410 A116411 A116412 * A116414 A116415 A116416 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 13 2006 STATUS approved

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Last modified June 6 05:06 EDT 2023. Contains 363139 sequences. (Running on oeis4.)