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A182069 Triangle of numbers 2^i*C(n,i) mod 3 converted to decimal. 4
1, 5, 13, 29, 142, 377, 757, 3785, 9841, 19685, 98422, 255905, 570862, 2795180, 7421206, 14901545, 74505454, 193720085, 387440173, 1937200865, 5036722249, 11235765017, 55016504566, 146064945221, 293292210961, 1466461054805, 3812798742493, 7625597484989 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Or, set x=3 in polynomial corresponding to A255285(n). - N. J. A. Sloane, Feb 21 2015
For k>=1, consider triangle for numbers k^i*C(n,i) with row sums (k+1)^n.
If one considers its entries modulo k+1, then we obtain Pascal triangle with the alternating signs within every row:
n/k.|..0.....1.....2.....3.....4.....5.....6.....7
==================================================
.0..|..1
.1..|..1.....-1
.2..|..1.....-2.....1
.3..|..1.....-3.....3.....-1
.4..|..1.....-4.....6.....-4.....1
.5..|..1.....-5....10....-10.....5....-1
.6..|
This is a common basis triangle for our generalizations. Consider the least positive residues of its entries modulo k+1 and read the rows as numbers in base k+1, converting to decimal. In case k=1 we obtain A001317. This sequence corresponds to k=2.
LINKS
FORMULA
For n>=0, a(3*n+2) = 13*a(3*n).
EXAMPLE
Consider the third row of the alternating Pascal triangle in comment: {1,-3,3,-1)={1,0,0,2} mod 3. We have (1002)_3=27+2=29. Thus a(3)=29.
MATHEMATICA
Table[FromDigits[Table[Mod[2^i Binomial[n, i], 3], {i, 0, n}], 3], {n, 0, 30}] (* T. D. Noe, Apr 10 2012 *)
CROSSREFS
Sequence in context: A147288 A146420 A147492 * A085555 A224888 A256314
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified May 24 05:24 EDT 2024. Contains 372772 sequences. (Running on oeis4.)