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A085691 T(n,k) is the number of triangles of side k in triangular matchstick arrangement of side n; n>=1 and k>=1. 1
1, 4, 1, 9, 3, 1, 16, 7, 3, 1, 25, 13, 6, 3, 1, 36, 21, 11, 6, 3, 1, 49, 31, 18, 10, 6, 3, 1, 64, 43, 27, 16, 10, 6, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{1}, {4,1}, {9, 3, 1}, {16, 7, 3, 1}, {25, 13, 6, 3, 1}

REFERENCES

J.H Conway and R.K Guy, The Book of Numbers,p.83.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

T(n, k) = 0 if n<k; T(n, k) = (n-k+1).(n-k+2)/2 if k<= n<2.(k-1); T(n, k)= n^2 - 3.(k-1).n + (5.k-4).(k-1)/2; Row sums = A002717; T(n, 1)=A000290, T(n, 2)give A002061; T(n, 3)give A010000

CROSSREFS

Cf. A002717, A000290, A002061, A010000.

Sequence in context: A260253 A261981 A153265 * A055461 A324999 A104796

Adjacent sequences:  A085688 A085689 A085690 * A085692 A085693 A085694

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jul 18 2003

STATUS

approved

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)