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A194271
Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194270.
22
0, 1, 4, 8, 16, 22, 24, 22, 40, 40, 32, 32, 56, 74, 96, 50, 88, 72, 32, 48, 72, 104, 128, 112, 144, 144, 152, 96, 152, 178, 240, 122, 184, 136, 32, 48, 72, 108, 144, 144, 184, 188, 200, 176, 272, 274, 416, 250, 288, 272, 216, 144, 208, 292, 384, 332, 376
OFFSET
0,3
COMMENTS
Essentially the first differences of A194270.
FORMULA
a(n) = n^2-(n-1)^2*(1-(-1)^n)/8, if 0 <= n <=4.
Let b(n) = A194441(n), let c(n) = A194443(n), let d(n) = A010694(n), then:
Conjecture: a(n) = 4*(b(n-1)-d(n)) + 2*(c(n)-d(n+1)) + 2*(c(n+2)-d(n+1)) + 8, if n >= 3.
Conjecture: a(2^k+2) = 32, if k >= 3.
EXAMPLE
Written as a triangle:
0,
1,
4,
8,
16,22,
24,22,40,40,
32,32,56,74,96,50,88,72,
32,48,72,104,128,112,144,144,152,96,152,178,240,122,184,136,
32,48,72,108,144,144,184,188,200,176,272,274,416,250,288,...
KEYWORD
nonn
AUTHOR
Omar E. Pol, Aug 23 2011
EXTENSIONS
More terms from Omar E. Pol, Sep 01 2011
STATUS
approved