OFFSET
0,2
COMMENTS
The former name, a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A027960, was in error with the data given. [This double summation gives A023537(n+1), or A027960(n+2, n+4) for n >= 0]. - G. C. Greubel, Jun 08 2025
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Philipp Emanuel Weidmann, The Sequencer OEIS Survey
Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).
FORMULA
a(n) = 2^(n+3) - Fibonacci(n+5) - Fibonacci(n+3).
a(n) = A101220(4, 2, n+1).
G.f.: (1+2*x)/((1-2*x)*(1-x-x^2)). - R. J. Mathar, Sep 22 2008
a(n) = 2*a(n-1) + A000032(n+1). - David A. Corneth, Apr 16 2015
a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3). - Colin Barker, Feb 17 2016
From G. C. Greubel, Jun 08 2025: (Start)
a(n) = 2^(n+3) - A000032(n+4).
E.g.f.: 8*exp(2*x) - exp(x/2)*( 7*cosh(sqrt(5)*x/2) + 3*sqrt(5)*sinh(sqrt(5)*x/2) ). (End)
MAPLE
with(combinat); f:=fibonacci; seq(2^(n+3) - f(n+5) - f(n+3), n=0..30); # G. C. Greubel, Sep 26 2019
MATHEMATICA
Table[2^(n+3) - LucasL[n+4], {n, 0, 30}] (* G. C. Greubel, Sep 26 2019 *)
PROG
(PARI) vector(31, n, f=fibonacci; 2^(n+2) - f(n+4) - f(n+2)) \\ G. C. Greubel, Sep 26 2019
(Magma) [2^(n+3) - Lucas(n+4): n in [0..30]]; // G. C. Greubel, Sep 26 2019
(SageMath)
def A027974(n): return 2**(n+3) - lucas_number2(n+4, 1, -1)
[A027974(n) for n in range(31)] # G. C. Greubel, Sep 26 2019; Jun 08 2025
(GAP) List([0..30], n-> 2^(n+3) - Lucas(1, -1, n+4)[2]); # G. C. Greubel, Sep 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved