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 A099462 Expansion of x/(1 - 4*x^2 - 4*x^3). 2
 0, 1, 0, 4, 4, 16, 32, 80, 192, 448, 1088, 2560, 6144, 14592, 34816, 82944, 197632, 471040, 1122304, 2674688, 6373376, 15187968, 36192256, 86245376, 205520896, 489750528, 1167065088, 2781085696, 6627262464, 15792603136, 37633392640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Binomial transform is A099463. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,4,4). FORMULA a(n) = 4*a(n-2) + 4*a(n-3). a(n) = Sum_{k=0..floor((n-1)/2)} binomial(k, n-2*k-1)*4^k. a(n+1) = Sum_{k=0..floor(n/2)} C((n-k)/2, k)*(1+(-1)^(n-k))*2^(n-k). - Paul Barry, Sep 09 2005 MATHEMATICA LinearRecurrence[{0, 4, 4}, {0, 1, 0}, 40] (* G. C. Greubel, Nov 18 2021 *) PROG (Magma) [n le 3 select (1+(-1)^n)/2 else 4*(Self(n-2) +Self(n-3)): n in [1..41]]; // G. C. Greubel, Nov 18 2021 (Sage) def a(n): return sum( 4^k*binomial(k, n-2*k-1) for k in (0..(n-1)//2) ) [a(n) for n in (0..40)] # G. C. Greubel, Nov 18 2021 CROSSREFS Cf. A099463. Sequence in context: A322039 A158101 A038234 * A218051 A092266 A257606 Adjacent sequences: A099459 A099460 A099461 * A099463 A099464 A099465 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 16 2004 STATUS approved

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Last modified December 7 14:20 EST 2022. Contains 358656 sequences. (Running on oeis4.)