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A045950
Number of upward triangles in a Star of David matchstick arrangement of size n.
2
0, 10, 59, 177, 394, 740, 1245, 1939, 2852, 4014, 5455, 7205, 9294, 11752, 14609, 17895, 21640, 25874, 30627, 35929, 41810, 48300, 55429, 63227, 71724, 80950, 90935, 101709, 113302, 125744, 139065, 153295, 168464, 184602, 201739, 219905, 239130, 259444
OFFSET
0,2
FORMULA
a(n) = n*(10*n^2+9*n+1)/2.
From Colin Barker, Dec 02 2014: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.
G.f.: x*(x^2+19*x+10) / (x-1)^4. (End)
E.g.f.: exp(x)*x*(20 + 39*x + 10*x^2)/2. - Stefano Spezia, Sep 18 2024
MATHEMATICA
A045950[n_] := n*(n*(10*n + 9) + 1)/2; Array[A045950, 50, 0] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {0, 10, 59, 177}, 50] (* Paolo Xausa, Sep 18 2024 *)
PROG
(PARI) concat(0, Vec(x*(x^2+19*x+10)/(x-1)^4 + O(x^100))) \\ Colin Barker, Dec 02 2014
CROSSREFS
Cf. A299965.
Sequence in context: A044148 A044529 A129330 * A226796 A061001 A055586
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name clarified by Paolo Xausa, Sep 19 2024
STATUS
approved