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A062136 Twelfth column of Losanitsch's triangle A034851 (formatted as lower triangular matrix). 3
1, 6, 42, 182, 693, 2184, 6216, 15912, 37854, 83980, 176484, 352716, 676270, 1248072, 2229096, 3863080, 6519591, 10737090, 17299646, 27313650, 42337659, 64512240, 96770544, 143048880, 208616044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also seventh column (m=6) of triangle A062135.

Number of homeomorphically irreducible (or series-reduced) trees (no vertices of degree 2) with n+9 leaves which become tree P(7) (path on 7 nodes (vertices) or 6 edges (links) when all leaves are omitted. A leave is an edge together with a node of degree 1 at one end. Proof by Polya enumeration. See illustration for A034851.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for sequences related to trees

FORMULA

G.f.: Pe(6, x^2)/((1-x)^(2*6)*(1+x)^6), with Pe(6, x^2) := sum(A034839(6, m)*x^(2*m), m=0..3)= 1+15*x^2+15*x^4+x^6.

a(n) = A034851(n+11,11).

a(2n+1) = A001288(2n+12)/2; a(2n) = (A001288(2n+11)+A000389(n+5))/2. [Gary W. Adamson, Dec 15 2010]

a(n) = (1/(2*11!))*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11) + (1/15)*(1/2^9)*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(1/2)*(1+(-1)^n). - Yosu Yurramendi, Jun 24 2013

MATHEMATICA

Table[(1/(2*11!))*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*(n + 8)*(n + 9)*(n + 10)*(n + 11) + (1/15)*(1/2^9)*(n + 2)*(n + 4)*(n + 6)*(n + 8)*(n + 10)*(1/2)*(1 + (-1)^n), {n, 0, 50}] (* G. C. Greubel, Nov 24 2017 *)

PROG

(PARI) for(n=0, 50, print1((1/(2*11!))*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*(n + 8)*(n + 9)*(n + 10)*(n + 11) + (1/15)*(1/2^9)*(n + 2)*(n + 4)*(n + 6)*(n + 8)*(n + 10)*(1/2)*(1 + (-1)^n), ", ")) \\ G. C. Greubel, Nov 24 2017

(MAGMA) [(1/(2*Factorial(11)))*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*(n + 8)*(n + 9)*(n + 10)*(n + 11) + (1/15)*(1/2^9)*(n + 2)*(n + 4)*(n + 6)*(n + 8)*(n + 10)*(1/2)*(1 + (-1)^n): n in [0..30]]; // G. C. Greubel, Nov 24 2017

CROSSREFS

Cf. A018213.

Sequence in context: A082986 A180806 A253946 * A047663 A054642 A321250

Adjacent sequences:  A062133 A062134 A062135 * A062137 A062138 A062139

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)