0,3

With a different offset, number of n-permutations of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly one u. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 28 2007

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

F. Ellermann, Illustration of binomial transforms

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 756

a(n)=sum{k=0..n, 5^(n-k)binomial(n-k+1, k)binomial(1, (k+1)/2)(1-(-1)^k)/2}. - Paul Barry (pbarry(AT)wit.ie), Oct 15 2004

a(n)=10a(n-1)-25a(n-2); n>1; a(0)=0, a(1)=1.

Fourth binomial transform of n (starting 0, 1, 10...) Convolution of powers of 5. G.f. x/(1-5x)^2; E.g.f.: xexp(5x) - Paul Barry (pbarry(AT)wit.ie), Jul 22 2003

G.f.: x/(1-10*x+25*x^2). [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]

a:=n->sum (5^n, j=0..n): seq(a(n), n=-1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007

seq(seq(binomial(i, j)*5^(i-1), j =i-1), i=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 28 2007

g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)*n/5, n=0..31); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]

a(n)=if(n<0, 0, n*5^(n-1)) /* Michael Somos Sep 12 2005 */

(Other) SAGE: [lucas_number2(n, 5, 0)*binomial(n, 1)/5^1 for n in xrange(0, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 11 2009]

(Other) sage: [lucas_number1(n, 10, 25) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]

Cf. A002697 and A027471.

Cf. A001787.

Sequence in context: A073379 A022734 A027203 this_sequence A111998 A026935 A110127

Adjacent sequences: A053461 A053462 A053463 this_sequence A053465 A053466 A053467

easy,nonn

Barry E. Williams, Jan 13 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 02 2000