|
|
A103142
|
|
a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=1, a(1)=2, a(3)=5, a(4)=13.
|
|
5
|
|
|
1, 2, 5, 13, 34, 88, 228, 591, 1532, 3971, 10293, 26680, 69156, 179256, 464641, 1204374, 3121801, 8091873, 20974562, 54367172, 140922580, 365278767, 946821848, 2454212215, 6361447625, 16489208080, 42740897848, 110786663616, 287164880785, 744346531114
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Row sums of generalized Pascal matrix A103141.
Generalized Pell numbers.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4).
G.f.: 1/(1 - 2*x - x^2 - x^3 - x^4).
|
|
MAPLE
|
m:=40; S:=series(1/(1-2*x-x^2-x^3-x^4), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Feb 12 2020
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) I:=[1, 2, 5, 13]; [n le 4 select I[n] else 2*Self(n-1)+Self(n-2)+Self(n-3) +Self(n-4): n in [1..40]]; // Vincenzo Librandi, Feb 05 2012
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-2*x-x^2-x^3-x^4) ).list()
(GAP) a:=[1, 2, 5, 13];; for n in [5..40] do a[n]:=2*a[n-1]+a[n-2]+a[n-3]+a[n-4]; od; a; # G. C. Greubel, Feb 12 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021
|
|
STATUS
|
approved
|
|
|
|