0,2

For n>3, the number of squares on the infinite 3-column half-strip chessboard at <=n knight moves from any fixed point on the short edge.

A008615(a(n)) = n. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2008

A157176(a(n)) = A001018(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]

Number of n permutations (n>=1) of 7 objects s, t, u, v, z, x, y, with repetition allowed, containing n-1 u's. Example: if n=1 then n-1=zero (0) u, a(1)=6 because we have s, t, v, z, x, y. if n=2 then n-1= one (1) u, a(2)=12 because we have su, tu, vu, zu, xu, yu, us, ut, uv, uz, ux, uy. if n=3 then n-1 =two (2) u, a(3)=18 because we have suu, usu, uus, tuu, utu, uut, vuu, uvu, uuv, zuu, uzu, uuz, xuu, uxu, uux, yuu, uyu, uuy. etc. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 17 2009]

Tanya Khovanova, Recursive Sequences

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 318

[ seq(6*n, n=0..45) ];

with(numtheory):tri := cfrac (sin(Pi/4), 50): a:=n->sum (nthdenom(tri, i)*nthnumer(tri, i), j=0..n): seq(a(n), n=-1..57); # and with(numtheory):tri := cfrac (sin(Pi/3), 60): a:=n->sum (nthdenom(tri, i)*nthnumer(tri, i)/7, j=0..n): seq(a(n), n=-1..57); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 08 2007

with(finance):seq(add(cashflows([1, 1, 4], 0 ), k=1..n), n=0..58); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008

with(finance):seq(add(cashflows([0, 0, 6], 0 ), k=1..n), n=0..58); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008

Table[Binomial[n, 1]*6^1, {n, 0, 58}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 17 2009]

(Other) 1.)sage: [crt(0, n, 3, 5) for n in xrange(0, 59)] # 2.)sage: [crt(6, n, 3, 5) for n in xrange(5, 65)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2009]

Essentially the same as A008458.

Cf. A016921, A016933, A016945, A016957, A016969.

Sequence in context: A121827 A126798 A008458 this_sequence A078596 A085129 A083263

Adjacent sequences: A008585 A008586 A008587 this_sequence A008589 A008590 A008591

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Second differences of A000578. - Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004