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 A172416 a(n) = 5*2^n/9 + 1/4 + (-1)^n*(n/6 + 7/36). 2
 1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136, 2278, 4549, 9105, 18202, 36412, 72815, 145639, 291268, 582546, 1165081, 2330173, 4660334, 9320680, 18641347, 37282707, 74565400, 149130814, 298261613, 596523241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The sequence and the 1st, 2nd, 3rd etc. difference form the array 1, 1, 3, 4, 10, 17, 37, 70, 144, 283, 571, 1136,.. 0, 2, 1, 6, 7, 20, 33, 74, 139, 288, 565, 1142, 2271,.. 2, -1, 5, 1, 13, 13, 41, 65, 149, 277, 577, 1129, 2285,.. -3, 6, -4, 12, 0, 28, 24, 84, 128, 300, 552, 1156,... where the sequence 1,2,5,12,.... = A045623 appears on the diagonal. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2). FORMULA a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4). a(n+1) - a(n) = A172285(n). a(2n) = A164044(n). a(2n+1) = A172447(n). a(n+1) - 2*a(n) = (-1)^(n+1)*A008619(n). G.f.: ( 1 - x^2 - x^3 ) / ( (2*x-1)*(x-1)*(1+x)^2 ). PROG (Magma) [5*2^n/9 +1/4 +(-1)^n*(n/6+7/36): n in [0..40]]; // Vincenzo Librandi, Aug 05 2011 CROSSREFS Sequence in context: A224073 A034774 A342536 * A317883 A337089 A144958 Adjacent sequences: A172413 A172414 A172415 * A172417 A172418 A172419 KEYWORD nonn,easy AUTHOR Paul Curtz, Feb 02 2010 STATUS approved

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Last modified September 29 20:23 EDT 2023. Contains 365777 sequences. (Running on oeis4.)