A055279 Number of rooted trees with n nodes and 4 leaves.

1, 4, 14, 39, 97, 212, 429, 804, 1427, 2406, 3900, 6094, 9245, 13645, 19682, 27791, 38530, 52516, 70521, 93390, 122157, 157945, 202104, 256090, 321628, 400567, 495070, 607445, 740362, 896657, 1079581, 1292574, 1539546, 1824621, 2152452, 2527932, 2956546

Offset

5,2

Links

Georg Fischer, Table of n, a(n) for n = 5..200

Index entries for sequences related to rooted trees

Formula

G.f.: x^5 * (1 + x + 3*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 5*x^6 + 2*x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)). - Michael Somos, Nov 02 2014

a(5-n) = A055365(n). for all n in Z. - Michael Somos, Nov 02 2014

0 = -30 + a(n) - 2*a(n+1) - a(n+2) + 3*a(n+3) + a(n+5) - 2*a(n+6) - 2*a(n+7) + a(n+8) + 3*a(n+10) - a(n+11) - 2*a(n+12) + a(n+13) for all n in Z. - Michael Somos, Nov 02 2014

a(n) ~ n^6 / 1152 as n -> infinity. - Michael Somos, Nov 02 2014

Example

G.f. = x^5 + 4*x^6 + 14*x^7 + 39*x^8 + 97*x^9 + 212*x^10 + 429*x^11 + ...

Prog

(PARI) {a(n) = if( n<5, n = -1-n; polcoeff( (1 + 2*x + 5*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 3*x^6 + x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) + x * O(x^n), n), n = n-5; polcoeff( (1 + x + 3*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 5*x^6 + 2*x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) + x * O(x^n), n))}; /* Michael Somos, Nov 02 2014 */

Crossrefs

Column 4 of A055277.

Cf. A055365.

Sequence in context: A130423 A266423 A055484 * A074083 A182819 A144141

Adjacent sequences: A055276 A055277 A055278 * A055280 A055281 A055282

Keyword

nonn

Author

Christian G. Bower, May 09 2000

Status

approved