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A133824 Triangle whose rows are sequences of increasing and decreasing fourth powers: 1; 1,16,1; 1,16,81,16,1; ... . 3
1, 1, 16, 1, 1, 16, 81, 16, 1, 1, 16, 81, 256, 81, 16, 1, 1, 16, 81, 256, 625, 256, 81, 16, 1, 1, 16, 81, 256, 625, 1296, 625, 256, 81, 16, 1, 1, 16, 81, 256, 625, 1296, 2401, 1296, 625, 256, 81, 16, 1, 1, 16, 81, 256, 625, 1296, 2401, 4096, 2401, 1296, 625, 256, 81, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Reading the triangle by rows produces the sequence 1,1,16,1,1,16,81,16,1,..., analogous to A004737.
From - Boris Putievskiy, Jan 13 2013: (Start)
The order of the list T(n,k) is by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1).
Row number k contains 2*k-1 numbers 1,16,...,(k-1)^4,k^4,(k-1)^4,...,16,1. (End)
LINKS
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.
FORMULA
O.g.f.: (1+qx)(1+11qx+11q^2x^2+q^3x^3)/((1-x)(1-qx)^4(1-q^2x)) = 1 + x(1 + 16q + q^2) + x^2(1 + 16q + 81q^2 + 16q^3 + q^4) + ... . Cf. 4th row of A008292.
From Boris Putievskiy, Jan 13 2013: (Start)
T(n,k) = min(n,k)^4.
a(n) = (A004737(n))^4.
a(n) = (A124258(n))^2.
a(n) = (floor(sqrt(n-1)) - |n- floor(sqrt(n-1))^2- floor(sqrt(n-1))-1| +1)^4. (End)
EXAMPLE
Triangle starts:
1;
1, 16, 1;
1, 16, 81, 16, 1;
1, 16, 81, 256, 81, 16, 1;
...
From Boris Putievskiy, Jan 13 2013: (Start)
The start of the sequence as table:
1...1...1...1...1.. .1...
1..16..16..16..16...16...
1..16..81..81..81...81...
1..16..81.256.256..256...
1..16..81.256.625..625...
1..16..81.256.625.1296...
...
(End)
MATHEMATICA
p4[n_]:=Module[{c=Range[n]^4}, Join[c, Rest[Reverse[c]]]]; Flatten[p4/@ Range[10]] (* Harvey P. Dale, Dec 08 2014 *)
CROSSREFS
Sequence in context: A245980 A040256 A245910 * A154228 A141697 A202750
KEYWORD
easy,nonn,tabf
AUTHOR
Peter Bala, Sep 25 2007
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)