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A292001
Number of (undirected) paths in the n-helm graph.
0
3, 26, 93, 260, 615, 1278, 2401, 4168, 6795, 10530, 15653, 22476, 31343, 42630, 56745, 74128, 95251, 120618, 150765, 186260, 227703, 275726, 330993, 394200, 466075, 547378, 638901, 741468, 855935, 983190, 1124153, 1279776, 1451043, 1638970, 1844605, 2069028
OFFSET
1,1
COMMENTS
Extended to a(1)-a(2) using the formula/recurrence.
FORMULA
a(n) = n*(-21 + 38*n - 12*n^2 + 4*n^3)/3.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(-3 - 11*x + 7*x^2 - 25*x^3)/(-1 + x)^5.
MATHEMATICA
Table[n (-21 + 38 n - 12 n^2 + 4 n^3)/3, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {3, 26, 93, 260, 615}, 20]
CoefficientList[Series[(-3 - 11 x + 7 x^2 - 25 x^3)/(-1 + x)^5, {x, 0, 20}], x]
CROSSREFS
Sequence in context: A294494 A048372 A269342 * A211622 A062124 A169832
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 07 2017
STATUS
approved