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 A079362 Sequence of sums of alternating powers of 3. 2
 1, 4, 5, 14, 17, 44, 53, 134, 161, 404, 485, 1214, 1457, 3644, 4373, 10934, 13121, 32804, 39365, 98414, 118097, 295244, 354293, 885734, 1062881, 2657204, 3188645, 7971614, 9565937, 23914844, 28697813, 71744534, 86093441, 215233604 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-3). FORMULA G.f.: x*(1+3*x-2*x^2)/((1-x)*(1-3*x^2)). - Michael Somos, Feb 18 2003 For n >= 1, a(2n-1) = (2/3)*3^n - 1, a(2n) = (5/3)*3^n - 1. - Benoit Cloitre, Feb 16 2003 MAPLE a[1]:=1:a[2]:=4:for n from 3 to 100 do a[n]:=3*a[n-2]+2 od: seq(a[n], n=1..33); # Zerinvary Lajos, Mar 17 2008 MATHEMATICA LinearRecurrence[{1, 3, -3}, {1, 4, 5}, 40] (* Harvey P. Dale, Oct 18 2016 *) PROG (PARI) a(n)=if(n<1, 0, 1+sum(k=2, n, 3^((k\2)-(k%2)))) (PARI) a(n)=if(n<0, 0, (5/3-3*n%2)*2^ceil(n/2)-1) (MAGMA) I:=[1, 4, 5]; [n le 3 select I[n] else Self(n-1) +3*Self(n-2) -3*Self(n-3): n in [1..40]]; // G. C. Greubel, Aug 07 2019 (Sage) @CachedFunction def a(n):     if (n==0): return 1     elif (1<=n<=2): return n+3     else: return a(n-1) + 3*a(n-2) - 3*a(n-3) [a(n) for n in (0..40)] # G. C. Greubel, Aug 07 2019 (GAP) a:=[1, 4, 5];; for n in [4..30] do a[n]:=a[n-1]+3*a[n-2]-3*a[n-3]; od; a; # G. C. Greubel, Aug 07 2019 CROSSREFS Cf. A079360, A079363, A028242, A048473 (bisection). Sequence in context: A191142 A049770 A262903 * A222364 A222372 A302348 Adjacent sequences:  A079359 A079360 A079361 * A079363 A079364 A079365 KEYWORD easy,nonn AUTHOR Cino Hilliard, Feb 15 2003 STATUS approved

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Last modified July 30 19:12 EDT 2021. Contains 346359 sequences. (Running on oeis4.)