|
| |
|
|
A114254
|
|
Sum of all terms on the two principal diagonals of a 2n+1 X 2n+1 ssquare spiral.
|
|
1
| |
|
|
1, 25, 101, 261, 537, 961, 1565, 2381, 3441, 4777, 6421, 8405, 10761, 13521, 16717, 20381, 24545, 29241, 34501, 40357, 46841, 53985, 61821, 70381, 79697, 89801, 100725, 112501, 125161, 138737, 153261, 168765, 185281, 202841, 221477, 241221
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| The 3 X 3 and 5 X 5 spirals are
7 8 9
6 1 2
5 4 3
and
21..22..23..24..25
20..7...8...9...10
19..6...1...2...11
18..5...4...3...12
17..16..15..14..13
|
|
|
FORMULA
| O.g.f.: 3/(-1+x)+16/(-1+x)^2+44/(-1+x)^3+32/(-1+x)^4 = (1+21*x+7*x^2+3*x^3)/(-1+x)^4 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 10 2008
a(n) = 1 + 10*n^2 + [(16n^3 + 26n)/3]. [Corrected by Arie Groeneveld (bradypus(at)xs4all.nl), Aug 17 2008]
|
|
|
PROG
| Python:
.l = input("Length of Diagonal? ")
.Sigma = 1 + 4*sum(4*k**2+k+3-2*((k+2)%(k+1)) for k in range(1, l+1))
.print Sigma
|
|
|
CROSSREFS
| Cf. A016754, A054569, A053755, A054554 for diagonals from origin.
Cf. A011655.
Sequence in context: A134422 A016850 A042220 * A042222 A158551 A044276
Adjacent sequences: A114251 A114252 A114253 * A114255 A114256 A114257
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| William A. Tedeschi (fynmun(AT)hotmail.com), Feb 06 2008, Mar 01 2008
|
| |
|
|
