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A028270
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Central elements in 3-Pascal triangle A028262 (by row).
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1
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1, 3, 8, 26, 90, 322, 1176, 4356, 16302, 61490, 233376, 890188, 3409588, 13104756, 50517200, 195234120, 756197910, 2934686610, 11408741520, 44420399100, 173191792620, 676104403260, 2642356838160, 10337529691320, 40481034410700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Or, start with Pascal's triangle; a(n) is the sum of the numbers on the periphery of the n-th central triangle containing exactly 3 numbers. The first three triangles are
...1...........2.........6
.1...1.......3...3.....10..10
and the corresponding sums are 3, 8 and 26. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 25 2003
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FORMULA
| G.f.: (x+1)/sqrt(1-4*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 08 2004
a(n)=binomial(2n, n)+binomial(2n-2, n-1)=A000984(n)+A000984(n-1) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 20 2004
a(n)=2binomial(2n-1, n-1)+binomial(2n-2, n-1)=binomial(2n, n)+binomial(2n-2, n-1)= A000984(n)+A000984(n-1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 20 2004
a(n) = (n+1)*C(n) + n*C(n-1), C = Catalan number (A000108). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2007
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MAPLE
| seq(binomial(2*n, n)+binomial(2*n-2, n-1), n=0..24);
seq(2*binomial(2*n-1, n-1)+binomial(2*n-2, n-1), n=1..24);
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CROSSREFS
| Cf. A081494, A081495, A081496, A000984.
Cf. A000108.
Sequence in context: A148817 A148818 A081497 * A124383 A148819 A148820
Adjacent sequences: A028267 A028268 A028269 * A028271 A028272 A028273
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KEYWORD
| nonn,easy
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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