A045950 Triangles in Star of David matchstick arrangement of side n.

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

Comments

This is 1/2 the sequence A299965 which counts both the 'standard' and the 'inverted' triangles. - John King, Apr 05 2019

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = n*(10*n^2+9*n+1)/2.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, Dec 02 2014

G.f.: x*(x^2+19*x+10) / (x-1)^4. - Colin Barker, Dec 02 2014

a(n) = A299965(n)/2. - John King, Apr 05 2019

Prog

(PARI) concat(0, Vec(x*(x^2+19*x+10)/(x-1)^4 + O(x^100))) \\ Colin Barker, Dec 02 2014

Crossrefs

Sequence in context: A044148 A044529 A129330 * A226796 A061001 A055586

Adjacent sequences: A045947 A045948 A045949 * A045951 A045952 A045953

Keyword

nonn,easy

Author

R. K. Guy

Status

approved