login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265226 Self-convolution of A257889. 2
1, 2, 5, 14, 34, 96, 261, 692, 1680, 4540, 12540, 34552, 92728, 251572, 662340, 1729628, 4261528, 11130160, 29802200, 80103640, 218398544, 595050400, 1621285648, 4411577744, 11776668772, 31899937136, 85998657296, 231056788736, 607876418544, 1615730650080, 4228062351360, 11047956392096, 27736466241312, 71915999814720, 188591683462784, 495344539985920, 1321221455067520, 3505058052234400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..2500

FORMULA

Terms satisfy:

(1) a(n) = A257889(2*n) / A257889(n),

(2) a(n+1) = A257889(2*n+1) / A257889(n),

(3) a(n) = Sum_{k=0..n} A257889(n-k) * A257889(k),

for n>=0, where A(x) = G(x)^2 and G(x) = Sum_{n>=0} A257889(n)*x^n.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 5*x^2 + 14*x^3 + 34*x^4 + 96*x^5 + 261*x^6 + 692*x^7 + 1680*x^8 + 4540*x^9 + 12540*x^10 + 34552*x^11 + 92728*x^12 +...

where

sqrt(A(x)) = 1 + x + 2*x^2 + 5*x^3 + 10*x^4 + 28*x^5 + 70*x^6 + 170*x^7 + 340*x^8 + 960*x^9 + 2688*x^10 + 7308*x^11 + 18270*x^12 +...+ A257889(n)*x^n +...

Illustration of initial terms:

a(1) = A257889(2)/A257889(1) = 2/1 = 2;

a(2) = A257889(3)/A257889(1) = 5/1 = 5;

a(2) = A257889(4)/A257889(2) = 10/2 = 5;

a(3) = A257889(5)/A257889(2) = 28/2 = 14;

a(3) = A257889(6)/A257889(3) = 70/5 = 14;

a(4) = A257889(7)/A257889(3) = 170/5 = 34;

a(4) = A257889(8)/A257889(4) = 340/10 = 34; ...

PROG

(PARI) {a(n) = my(A=1+x); for(k=2, n, A = A + a(k\2) * polcoeff(A^2, (k+1)\2) * x^k +x*O(x^n) ); polcoeff(A^2, n)}

for(n=0, 40, print1(a(n), ", "))

(PARI) {a(n) = my(A=[1, 1]); for(k=2, n, A = concat(A, A[k\2+1]*Vec(Ser(A)^2)[(k+1)\2+1]) ); Vec(Ser(A)^2)[n+1]}

for(n=0, 40, print1(a(n), ", "))

(PARI) /* Generates N terms rather quickly: */

N=300; A=[1, 1]; for(k=2, N, A = concat(A, A[k\2+1]*Vec(Ser(A)^2)[(k+1)\2+1]) ); Vec(Ser(A)^2)

CROSSREFS

Cf. A257889.

Sequence in context: A090803 A018015 A080039 * A299164 A131408 A137917

Adjacent sequences:  A265223 A265224 A265225 * A265227 A265228 A265229

KEYWORD

nonn,look

AUTHOR

Paul D. Hanna, Dec 15 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 04:02 EDT 2018. Contains 316259 sequences. (Running on oeis4.)